/// LSU EE 4702-1 (Fall 2016), GPU Programming // /// Homework 3 and 4 --- SOLUTION PRELIMINARY // // See http://www.ece.lsu.edu/koppel/gpup/2016/hw03.pdf /// Purpose // // Demonstrate simulation of point masses connected by springs. /// What Code Does // Simulates balls connected by springs over a platform. Balls and // springs can be initialized in different arrangements (called // scenes). Currently scene 1 is a simple string of beads, and scenes // 2, 3, and 4 are trusses. The platform consists of tiles, some are // purple-tinted mirrors (showing a reflection of the ball), the // others show the course syllabus. /// Keyboard Commands // /// Object (Eye, Light, Ball) Location or Push // Arrows, Page Up, Page Down // Move object or push ball, depending on mode. // With shift key pressed, motion is 5x faster. // 'e': Move eye. // 'l': Move light. // 'b': Move head (first) ball. (Change position but not velocity.) // 'B': Push head ball. (Add velocity.) // /// Eye Direction // Home, End, Delete, Insert // Turn the eye direction. // Home should rotate eye direction up, End should rotate eye // down, Delete should rotate eye left, Insert should rotate eye // right. The eye direction vector is displayed in the upper left. /// Simulation Options // (Also see variables below.) // // 'w' Twirl balls around axis formed by head and tail. (Prob 2 soln). // '1' Set up scene 1. // '2' Set up scene 2. // '3' Set up scene 3. // 'p' Pause simulation. (Press again to resume.) // ' ' (Space bar.) Advance simulation by 1/30 second. // 'S- ' (Shift-space bar.) Advance simulation by one time step. // 'h' Freeze position of first (head) ball. (Press again to release.) // 't' Freeze position of last (tail) ball. (Press again to release.) // 's' Stop balls. // 'g' Turn gravity on and off. // 'y' Toggle value of opt_tryout1. Intended for experiments and debugging. // 'Y' Toggle value of opt_tryout2. Intended for experiments and debugging. // 'F11' Change size of green text (in upper left). // 'F12' Write screenshot to file. // 'z' Switch between render_link_1 and render_link_2. /// Variables // Selected program variables can be modified using the keyboard. // Use "Tab" to cycle through the variable to be modified, the // name of the variable is displayed next to "VAR" on the bottom // line of green text. // 'Tab' Cycle to next variable. // '`' Cycle to previous variable. // '+' Increase variable value. // '-' Decrease variable value. // // VAR Spring Constant - Set spring constant. // VAR Time Step Duration - Set physics time step. // VAR Air Resistance - Set air resistance. // VAR Light Intensity - The light intensity. // VAR Gravity - Gravitational acceleration. (Turn on/off using 'g'.) #define GL_GLEXT_PROTOTYPES #define GLX_GLXEXT_PROTOTYPES #include <GL/gl.h> #include <GL/glext.h> #include <GL/glx.h> #include <GL/glxext.h> #include <GL/glu.h> #include <GL/freeglut.h> #include <gp/util.h> #include <gp/glextfuncs.h> #include <gp/coord.h> #include <gp/shader.h> #include <gp/pstring.h> #include <gp/misc.h> #include <gp/gl-buffer.h> #include <gp/texture-util.h> #include <gp/colors.h> #include "util-containers.h" #include "shapes.h" /// /// Main Data Structures /// // // class World: All data about scene. class World; // Object Holding Ball State // class Ball { public: Ball():velocity(pVect(0,0,0)),omega(pVect(0,0,0)), density(1.00746), fdt_to_do(0), locked(false), color(color_lsu_spirit_gold),contact(false) { orientation_set(pVect(0,1,0),0); } pCoor position; pVect velocity; pQuat orientation; pMatrix3x3 omatrix; pVect omega; // Spin rate and axis. int idx; // Position in balls_pos_rad; float mass; float mass_min; // Mass below which simulation is unstable. float radius; float radius_sq, radius_inv; // Pre-computed based on radius. float density; float mass_inv; float fdt_to_do; // Radius / moment of inertia. bool locked; pVect force; pVect torque; pColor color; bool contact; // When true, ball rendered in gray. float spring_constant_sum; // Used to compute minimum mass. void orientation_set(pNorm dir, float angle) { orientation_set(pQuat(dir,angle)); } void orientation_set(pQuat ori) { orientation = ori; omatrix = pMatrix3x3_Rotation(orientation); } void constants_update(); pVect point_rot_vel(pNorm tact_dir); pVect point_rot_vel(pVect tact_dir); void apply_tan_force(pNorm tact_dir, pNorm force_dir, double force_mag); void push(pVect amt); void translate(pVect amt); void stop(); void freeze(); }; void Ball::constants_update() { assert( radius ); radius_sq = radius * radius; mass = 4.0 / 3 * M_PI * radius_sq * radius * density; radius_inv = 1 / radius; mass_inv = 1 / mass; // FYI, notice simplifications: // const float mo_inertia = 0.4 * mass * radius_sq; // fdt_to_do = radius / mo_inertia; fdt_to_do = radius_inv * 2.5 * mass_inv; } pVect Ball::point_rot_vel(pNorm direction) { /// Return velocity of point on surface of ball. // return radius * cross( omega, direction ); } pVect Ball::point_rot_vel(pVect rel_pos) { /// Return velocity of point relative to center. // return cross( omega, rel_pos ); } void Ball::apply_tan_force(pNorm tact_dir, pNorm force_dir, double force_mag) { torque += cross(tact_dir, force_mag * force_dir); } class Link { public: Link(Ball *b1, Ball *b2):ball1(b1),ball2(b2), snapped(false), natural_color(color_lsu_spirit_purple),color(color_lsu_spirit_purple) { init(); } Link(Ball *b1, Ball *b2, pColor colorp):ball1(b1),ball2(b2), snapped(false), natural_color(colorp),color(colorp) { init(); } Link(Link *link, pVect cb1p, pVect cb2p, float drp): ball1(link->ball1), ball2(link->ball2), cb1(cb1p), cb2(cb2p), is_surface_connection(true), is_renderable(false), is_simulatable(true), distance_relaxed(drp), snapped(false){ link->is_simulatable = false; } void init() { assert( ball1->radius > 0 ); assert( ball2->radius > 0 ); is_simulatable = true; is_renderable = true; pNorm n12(ball1->position,ball2->position); const float rad_sum = ball1->radius + ball2->radius; is_surface_connection = n12.magnitude >= rad_sum; if ( !is_surface_connection ) { distance_relaxed = n12.magnitude; cb1 = cb2 = pVect(0,0,0); return; } distance_relaxed = n12.magnitude - rad_sum; cb1 = ball1->radius * mult_MTV( ball1->omatrix, n12 ); cb2 = ball2->radius * mult_MTV( ball2->omatrix, -n12 ); } int serial; Ball* const ball1; Ball* const ball2; pVect cb1, cb2, b1_dir, b2_dir; bool is_surface_connection; bool is_renderable, is_simulatable; float distance_relaxed; bool snapped; pColor natural_color; pColor color; }; // Declare containers and iterators for Balls and Links. // (See util_container.h.) // typedef pVectorI<Link> Links; typedef pVectorI_Iter<Link> LIter; typedef pVectorI<Ball> Balls; typedef pVectorI_Iter<Ball> BIter; typedef pVector<pVect> pVects; typedef pVector<pCoor> pCoors; enum Render_Option { RO_Normally, RO_Simple, RO_Shadow_Volumes }; enum Shader_Option { SO_Fixed, SO_Phong, SO_ENUM_SIZE }; class World { public: World(pOpenGL_Helper &fb):ogl_helper(fb){init();} void init(); void init_graphics(); static void frame_callback_w(void *moi){((World*)moi)->frame_callback();} void frame_callback(); void render(); void render_objects(Render_Option render_option); void objects_erase(); void cb_keyboard(); void modelview_update(); pOpenGL_Helper& ogl_helper; pVariable_Control variable_control; pFrame_Timer frame_timer; double world_time; double last_frame_wall_time; float opt_time_step_duration; int time_step_count; float opt_gravity_accel; // Value chosen by user. pVect gravity_accel; // Set to zero when opt_gravity is false; bool opt_gravity; bool opt_head_lock, opt_tail_lock; bool opt_ride; // When true, move eye to ball_eye. bool opt_tryout1, opt_tryout2; // For ad-hoc experiments. bool opt_ball_texture; // Tiled platform for ball. // float platform_xmin, platform_xmax, platform_zmin, platform_zmax; float platform_pi_xwidth_inv; pBuffer_Object<pVect> platform_tile_coords; pBuffer_Object<float> platform_tex_coords; pVect platform_normal; GLuint texid_hw; GLuint texid_syl; GLuint texid_emacs; bool opt_platform_texture; void platform_update(); bool platform_collision_possible(pCoor pos); pCoor light_location; float opt_light_intensity; enum { MI_Eye, MI_Light, MI_Ball, MI_Ball_V, MI_COUNT } opt_move_item; bool opt_pause; bool opt_single_frame; // Simulate for one frame. bool opt_single_time_step; // Simulate for one time step. int viewer_shadow_volume; pCoor eye_location; pVect eye_direction; pMatrix modelview; pMatrix transform_mirror; pVect adj_vector; double adj_t_prev; double adj_t_stop; double adj_duration; int opt_shader; bool opt_shadows; pShader *sp_fixed; // Fixed functionality. pShader *sp_phong; // Basic stuff. GLuint balls_pos_rad_bo; GLuint balls_color_bo; GLuint links_indices_bo; pColor *balls_color; pCoor *balls_pos_rad; size_t balls_size; size_t links_size; int last_setup; // Last scene set up. bool link_change; void ball_setup_1(); void ball_setup_2(); void ball_setup_3(); void ball_setup_4(); void ball_setup_5(); void setup_at_end(); void time_step_cpu(double); void balls_stop(); void balls_freeze(); void balls_translate(pVect amt, int idx); void balls_translate(pVect amt); void balls_push(pVect amt, int idx); void balls_push(pVect amt); void balls_twirl(); void lock_update(); Ball *make_marker(pCoor pos, pColor col); Ball *ball_eye, *ball_gaze, *ball_down; float opt_spring_constant; float opt_air_resistance; float distance_relaxed; int chain_length; Balls balls; Ball *head_ball, *tail_ball; Links links; Sphere sphere; Cylinder cyl; /// 2016 Homework 3 // Links link_new(Ball *ball1, Ball *ball2); void render_link_1(Link *link); void render_link_2(Link *link); int opt_render_links; /// Homework 4: This is a good place to declare items needed across calls. /// SOLUTION -- Homework 4 // // Buffer objects for attributes of curved links. GLuint link_bo_vtx, link_bo_nrm, link_bo_tco; // Buffer objects for attributes of straight links. GLuint link_bo_vtx_s, link_bo_nrm_s; // Number of vertices in curved links. int bo_s_num_vertices; // Transformation matrix transforming saved straight link to a local space. pMatrix link_s_to_local; }; void World::init_graphics() { /// /// Graphical Model Initialization /// balls_pos_rad = NULL; balls_pos_rad_bo = 0; balls_color = NULL; balls_color_bo = 0; balls_size = 0; links_size = 0; link_change = true; opt_platform_texture = true; opt_head_lock = false; opt_tail_lock = false; opt_ball_texture = true; opt_tryout1 = opt_tryout2 = false; eye_location = pCoor(24.2,11.6,-38.7); eye_direction = pVect(-0.42,-0.09,0.9); platform_xmin = -40; platform_xmax = 40; platform_zmin = -40; platform_zmax = 40; texid_syl = pBuild_Texture_File("gpup.png",false,255); texid_emacs = pBuild_Texture_File("mult.png", false,-1); texid_hw = pBuild_Texture_File("hw03-assign.png", false,255); opt_light_intensity = 100.2; light_location = pCoor(platform_xmax,platform_xmax,platform_zmin); variable_control.insert(opt_light_intensity,"Light Intensity"); opt_move_item = MI_Eye; opt_pause = false; opt_single_time_step = false; opt_single_frame = false; sphere.init(35); platform_update(); modelview_update(); adj_t_stop = 0; adj_duration = 0.25; opt_render_links = 0; /// SOLUTION -- Homework 4 link_bo_vtx = 0; bo_s_num_vertices = 0; } void World::platform_update() { const float tile_count = 19; const float ep = 1.00001; const float delta_x = ( platform_xmax - platform_xmin ) / tile_count * ep; const float zdelta = ( platform_zmax - platform_zmin ) / tile_count * ep; const float trmin = 0.05; const float trmax = 0.7; const float tsmin = 0; const float tsmax = 0.4; platform_normal = pVect(0,1,0); PStack<pVect> p_tile_coords; PStack<pVect> p1_tile_coords; PStack<float> p_tex_coords; bool even = true; for ( int i = 0; i < tile_count; i++ ) { const float x0 = platform_xmin + i * delta_x; const float x1 = x0 + delta_x; const float y = 0; for ( float z = platform_zmin; z < platform_zmax; z += zdelta ) { PStack<pVect>& t_coords = even ? p_tile_coords : p1_tile_coords; p_tex_coords += trmax; p_tex_coords += tsmax; t_coords += pVect(x0,y,z); p_tex_coords += trmax; p_tex_coords += tsmin; t_coords += pVect(x0,y,z+zdelta); p_tex_coords += trmin; p_tex_coords += tsmin; t_coords += pVect(x1,y,z+zdelta); p_tex_coords += trmin; p_tex_coords += tsmax; t_coords += pVect(x1,y,z); even = !even; } } while ( pVect* const v = p1_tile_coords.iterate() ) p_tile_coords += *v; platform_tile_coords.re_take(p_tile_coords); platform_tile_coords.to_gpu(); platform_tex_coords.re_take(p_tex_coords); platform_tex_coords.to_gpu(); } void World::modelview_update() { pMatrix_Translate center_eye(-eye_location); pMatrix_Rotation rotate_eye(eye_direction,pVect(0,0,-1)); modelview = rotate_eye * center_eye; pMatrix reflect; reflect.set_identity(); reflect.rc(1,1) = -1; transform_mirror = modelview * reflect * invert(modelview); } void World::render_objects(Render_Option option) { const float shininess_ball = 5; pColor spec_color(0.2,0.2,0.2); if ( option == RO_Shadow_Volumes ) viewer_shadow_volume = 0; if ( option == RO_Normally ) { glLightf(GL_LIGHT0, GL_LINEAR_ATTENUATION, 1.0); if ( opt_ball_texture ) { glEnable(GL_TEXTURE_2D); glBindTexture(GL_TEXTURE_2D,texid_emacs); } else { glDisable(GL_TEXTURE_2D); } glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,shininess_ball); glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,spec_color); glLightModeli(GL_LIGHT_MODEL_COLOR_CONTROL, GL_SEPARATE_SPECULAR_COLOR); glEnable(GL_COLOR_SUM); } cyl.apex_radius = 1; cyl.set_color(color_lsu_spirit_purple); if ( option == RO_Shadow_Volumes ) { #ifdef DB_SV glLightf(GL_LIGHT0, GL_LINEAR_ATTENUATION, 1.0); glEnable(GL_COLOR_SUM); glColor3f(0.5,0,0); #endif cyl.light_pos = light_location; sphere.light_pos = light_location; for ( BIter ball(balls); ball; ) sphere.render_shadow_volume(ball->radius,ball->position); for ( LIter link(links); link; ) { if ( link->snapped ) continue; if ( !link->is_renderable ) continue; if ( !link->is_simulatable ) continue; // Should check if straight. Ball *const ball1 = link->ball1; Ball *const ball2 = link->ball2; cyl.render_shadow_volume (ball1->position,0.3*ball1->radius, ball2->position-ball1->position); } } else { sphere.opt_texture = opt_ball_texture; if ( opt_shader == SO_Phong ) sp_phong->use(); else if ( opt_shader == SO_Fixed ) sp_fixed->use(); if ( opt_shader != SO_Fixed ) { glUniform2i(3, opt_tryout1, opt_tryout2); } for ( BIter ball(balls); ball; ) { if ( ball->contact ) sphere.color = color_gray; else if ( ball->mass > 0 && ball->mass < ball->mass_min ) sphere.color = color_red; else if ( ball->mass > 0 && ball->locked ) sphere.color = color_pale_green; else sphere.color = ball->color; sphere.render (ball->radius,ball->position, pMatrix_Rotation(ball->orientation)); } glBindTexture(GL_TEXTURE_2D,texid_hw); for ( Link *link: links ) { if ( !link->is_renderable ) continue; if ( opt_render_links == 0 ) render_link_1(link); else render_link_2(link); continue; Ball *const ball1 = link->ball1; Ball *const ball2 = link->ball2; pVect dir1 = ball1->omatrix * link->cb1; pCoor pos1 = ball1->position + dir1; pVect dir2 = ball2->omatrix * link->cb2; pCoor pos2 = ball2->position + dir2; cyl.set_color(link->color); cyl.render(pos1,0.3*ball1->radius, pos2-pos1); } } sp_fixed->use(); glDisable(GL_COLOR_SUM); glLightModeli(GL_LIGHT_MODEL_COLOR_CONTROL, GL_SINGLE_COLOR); glLightfv(GL_LIGHT0, GL_SPECULAR, color_black); // // Render Platform // const int half_elements = platform_tile_coords.elements >> 3 << 2; glEnable(GL_TEXTURE_2D); // Set up attribute (vertex, normal, etc.) arrays. // glBindTexture(GL_TEXTURE_2D,texid_syl); platform_tile_coords.bind(); glVertexPointer(3, GL_FLOAT, sizeof(platform_tile_coords.data[0]), 0); glEnableClientState(GL_VERTEX_ARRAY); glNormal3fv(platform_normal); platform_tex_coords.bind(); glTexCoordPointer(2, GL_FLOAT,2*sizeof(float), 0); glEnableClientState(GL_TEXTURE_COORD_ARRAY); // Write lighter-colored, textured tiles. // glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,spec_color); glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,2.0); glColor3f(0.35,0.35,0.35); glColor3f(0.55,0.55,0.55); glDrawArrays(GL_QUADS,0,half_elements+4); glDisableClientState(GL_VERTEX_ARRAY); glDisableClientState(GL_TEXTURE_COORD_ARRAY); glBindBuffer(GL_ARRAY_BUFFER,0); } void World::render() { // Get any waiting keyboard commands. // cb_keyboard(); // Start a timer object used for tuning this code. // frame_timer.frame_start(); /// Emit a Graphical Representation of Simulation State // // Understanding of the code below not required for introductory // lectures. // That said, much of the complexity of the code is to show // the ball shadow and reflection. const int win_width = ogl_helper.get_width(); const int win_height = ogl_helper.get_height(); const float aspect = float(win_width) / win_height; glMatrixMode(GL_MODELVIEW); glLoadTransposeMatrixf(modelview); glMatrixMode(GL_PROJECTION); glLoadIdentity(); // Frustum: left, right, bottom, top, near, far glFrustum(-.8,.8,-.8/aspect,.8/aspect,1,5000); glViewport(0, 0, win_width, win_height); pError_Check(); glClearColor(0,0,0,0.5); glClearDepth(1.0); glClearStencil(0); glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT | GL_STENCIL_BUFFER_BIT ); glEnable(GL_DEPTH_TEST); glDepthFunc(GL_LESS); glDisable(GL_BLEND); glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,1); glLightfv(GL_LIGHT0, GL_POSITION, light_location); glLightf(GL_LIGHT0, GL_CONSTANT_ATTENUATION, 0.5); glLightf(GL_LIGHT0, GL_LINEAR_ATTENUATION, 1.0); glLightf(GL_LIGHT0, GL_QUADRATIC_ATTENUATION, 0); pColor ambient_color(0x555555); glLightModelfv(GL_LIGHT_MODEL_AMBIENT, ambient_color); glLightfv(GL_LIGHT0, GL_DIFFUSE, color_white * opt_light_intensity); glLightfv(GL_LIGHT0, GL_AMBIENT, color_black); glLightfv(GL_LIGHT0, GL_SPECULAR, color_white * opt_light_intensity); glEnable(GL_LIGHT0); glEnable(GL_LIGHTING); glEnable(GL_COLOR_MATERIAL); glColorMaterial(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE); glShadeModel(GL_SMOOTH); // Common to all textures. // glActiveTexture(GL_TEXTURE0); glEnable(GL_TEXTURE_2D); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MIN_FILTER, GL_LINEAR_MIPMAP_LINEAR); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MAG_FILTER,GL_LINEAR); glTexEnvi(GL_TEXTURE_ENV,GL_TEXTURE_ENV_MODE,GL_MODULATE); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_WRAP_S,GL_REPEAT); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_WRAP_T,GL_REPEAT); glEnable(GL_RESCALE_NORMAL); glEnable(GL_NORMALIZE); const double time_now = time_wall_fp(); const bool blink_visible = int64_t(time_now*3) & 1; # define BLINK(txt,pad) ( blink_visible ? txt : pad ) ogl_helper.fbprintf("%s\n",frame_timer.frame_rate_text_get()); ogl_helper.fbprintf ("Code Compiled: %s\n", #ifdef __OPTIMIZE__ "WITH OPTIMIZATION" #else BLINK("WITHOUT OPTIMIZATION","") #endif ); ogl_helper.fbprintf ("Time Step: %8d World Time: %11.6f %s\n", time_step_count, world_time, opt_pause ? BLINK("PAUSED, 'p' to unpause, SPC or S-SPC to step.","") : "Press 'p' to pause." ); ogl_helper.fbprintf ("Eye location: [%5.1f, %5.1f, %5.1f] " "Eye direction: [%+.2f, %+.2f, %+.2f]\n", eye_location.x, eye_location.y, eye_location.z, eye_direction.x, eye_direction.y, eye_direction.z); Ball& ball = *balls[0]; ogl_helper.fbprintf ("Head Ball Pos [%5.1f,%5.1f,%5.1f] Vel [%+5.1f,%+5.1f,%+5.1f]\n", ball.position.x,ball.position.y,ball.position.z, ball.velocity.x,ball.velocity.y,ball.velocity.z ); ogl_helper.fbprintf ("Links: %s ('z' to change) " "Tryout 1: %s ('y' to change) Tryout 2: %s ('Y' to change)\n", opt_render_links == 0 ? "render_link_1" : "render_link_2", opt_tryout1 ? BLINK("ON"," ") : "OFF", opt_tryout2 ? BLINK("ON"," ") : "OFF"); pVariable_Control_Elt* const cvar = variable_control.current; ogl_helper.fbprintf("VAR %s = %.5f (TAB or '`' to change, +/- to adjust)\n", cvar->name,cvar->get_val()); const int half_elements = platform_tile_coords.elements >> 3 << 2; // // Render ball reflection. (Will be blended with dark tiles.) // // Write stencil at location of dark (mirrored) tiles. // glDisable(GL_LIGHTING); glEnable(GL_STENCIL_TEST); glStencilFunc(GL_NEVER,2,2); glStencilOp(GL_REPLACE,GL_KEEP,GL_KEEP); platform_tile_coords.bind(); glVertexPointer(3, GL_FLOAT, sizeof(platform_tile_coords.data[0]), 0); glEnableClientState(GL_VERTEX_ARRAY); glDrawArrays(GL_QUADS,half_elements+4,half_elements-4); glEnable(GL_LIGHTING); glDisableClientState(GL_VERTEX_ARRAY); glBindBuffer(GL_ARRAY_BUFFER,0); // Prepare to write only stenciled locations. // glStencilFunc(GL_EQUAL,2,2); glStencilOp(GL_KEEP,GL_KEEP,GL_KEEP); // Use a transform that reflects objects to other side of platform. // glMatrixMode(GL_PROJECTION); glPushMatrix(); glMultTransposeMatrixf(transform_mirror); // Reflected front face should still be treated as the front face. // glFrontFace(GL_CW); render_objects(RO_Normally); glFrontFace(GL_CCW); glMatrixMode(GL_PROJECTION); glPopMatrix(); glDisable(GL_STENCIL_TEST); // Setup texture for platform. // glBindTexture(GL_TEXTURE_2D,texid_syl); // Blend dark tiles with existing ball reflection. // glEnable(GL_STENCIL_TEST); glBlendEquation(GL_FUNC_ADD); glBlendFunc(GL_CONSTANT_ALPHA,GL_ONE_MINUS_CONSTANT_ALPHA); // src, dst glBlendColor(0,0,0,0.5); glDepthFunc(GL_ALWAYS); if ( opt_platform_texture ) { glEnable(GL_TEXTURE_2D); platform_tex_coords.bind(); glTexCoordPointer(2, GL_FLOAT,2*sizeof(float), 0); glEnableClientState(GL_TEXTURE_COORD_ARRAY); } platform_tile_coords.bind(); glVertexPointer (3, GL_FLOAT,sizeof(platform_tile_coords.data[0]), 0); glEnableClientState(GL_VERTEX_ARRAY); glNormal3fv(platform_normal); if ( opt_platform_texture ) glEnable(GL_TEXTURE_2D); // Write lighter-colored, textured tiles. // glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,color_gray); glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,2.0); glColor3f(0.35,0.35,0.35); glDrawArrays(GL_QUADS,0,half_elements+4); // Write darker-colored, untextured, mirror tiles. // glEnable(GL_BLEND); glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,color_white); glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,20); glDisable(GL_TEXTURE_2D); glColor3fv(color_lsu_spirit_purple); glDrawArrays(GL_QUADS,half_elements+4,half_elements-4); glDisable(GL_BLEND); glDisableClientState(GL_TEXTURE_COORD_ARRAY); glDisableClientState(GL_VERTEX_ARRAY); glBindBuffer(GL_ARRAY_BUFFER,0); glDisable(GL_STENCIL_TEST); glDepthFunc(GL_LESS); glLightModelfv(GL_LIGHT_MODEL_AMBIENT, ambient_color); if ( !opt_shadows ) { // Render. // render_objects(RO_Normally); } else { // // First pass, render using only ambient light. // glDisable(GL_LIGHT0); // Send balls, tiles, and platform to opengl. // Do occlusion test too. // render_objects(RO_Normally); // // Second pass, add on light0. // // Turn off ambient light, turn on light 0. // glLightModelfv(GL_LIGHT_MODEL_AMBIENT, color_black); glEnable(GL_LIGHT0); glClear(GL_STENCIL_BUFFER_BIT); // Make sure that only stencil buffer written. // #ifndef DB_SV glColorMask(false,false,false,false); glDepthMask(false); // Don't waste time computing lighting. // glDisable(GL_LIGHTING); #endif glDisable(GL_TEXTURE_2D); // Set up stencil test to count shadow volume surfaces: plus 1 for // entering the shadow volume, minus 1 for leaving the shadow // volume. // glEnable(GL_STENCIL_TEST); // sfail, dfail, dpass glStencilOpSeparate(GL_FRONT,GL_KEEP,GL_KEEP,GL_INCR_WRAP); glStencilOpSeparate(GL_BACK,GL_KEEP,GL_KEEP,GL_DECR_WRAP); glStencilFuncSeparate(GL_FRONT_AND_BACK,GL_ALWAYS,1,-1); // ref, mask // Write stencil with shadow locations based on shadow volumes // cast by light0 (light_location). Shadowed locations will // have a positive stencil value. Routine will set viewer_shadow_volume // to the number of view volumes containing the eye. // render_objects(RO_Shadow_Volumes); glEnable(GL_LIGHTING); glColorMask(true,true,true,true); glDepthMask(true); // Use stencil test to prevent writes to shadowed areas. // glStencilOp(GL_KEEP,GL_KEEP,GL_KEEP); glStencilFunc(GL_EQUAL,viewer_shadow_volume,-1); // ref, mask // Allow pixels to be re-written. // glDepthFunc(GL_LEQUAL); glEnable(GL_BLEND); glBlendEquation(GL_FUNC_ADD); glBlendFunc(GL_ONE,GL_ONE); // Render. // render_objects(RO_Normally); glDisable(GL_BLEND); glDisable(GL_STENCIL_TEST); } // Render Marker for Light Source // insert_tetrahedron(light_location,0.5); pError_Check(); glColor3f(0.5,1,0.5); frame_timer.frame_end(); ogl_helper.user_text_reprint(); glutSwapBuffers(); } void World::cb_keyboard() { if ( !ogl_helper.keyboard_key ) return; pVect adjustment(0,0,0); pVect user_rot_axis(0,0,0); const bool shift = ogl_helper.keyboard_shift; const float move_amt = shift ? 2.0 : 0.4; switch ( ogl_helper.keyboard_key ) { case FB_KEY_LEFT: adjustment.x = -move_amt; break; case FB_KEY_RIGHT: adjustment.x = move_amt; break; case FB_KEY_PAGE_UP: adjustment.y = move_amt; break; case FB_KEY_PAGE_DOWN: adjustment.y = -move_amt; break; case FB_KEY_DOWN: adjustment.z = move_amt; break; case FB_KEY_UP: adjustment.z = -move_amt; break; case FB_KEY_DELETE: user_rot_axis.y = 1; break; case FB_KEY_INSERT: user_rot_axis.y = -1; break; case FB_KEY_HOME: user_rot_axis.x = 1; break; case FB_KEY_END: user_rot_axis.x = -1; break; case '1': ball_setup_1(); break; case '2': ball_setup_2(); break; case '3': ball_setup_3(); break; case '4': ball_setup_4(); break; case '5': ball_setup_5(); break; case 'b': opt_move_item = MI_Ball; break; case 'B': opt_move_item = MI_Ball_V; break; case 'e': case 'E': opt_move_item = MI_Eye; break; case 'g': case 'G': opt_gravity = !opt_gravity; break; case 'h': case 'H': opt_head_lock = !opt_head_lock; break; case 't': case 'T': opt_tail_lock = !opt_tail_lock; break; case 'l': case 'L': opt_move_item = MI_Light; break; case 'n': case 'N': opt_platform_texture = !opt_platform_texture; break; case 'p': case 'P': opt_pause = !opt_pause; break; case 'r': case 'R': opt_ride = !opt_ride; break; case 's': case 'S': balls_stop(); break; case 'v': case 'V': opt_shader++; if ( opt_shader > 1 ) opt_shader = 0; break; case 'w': case 'W': balls_twirl(); break; case 'y': opt_tryout1 = !opt_tryout1; break; case 'Y': opt_tryout2 = !opt_tryout2; break; case 'z': opt_render_links++; if ( opt_render_links > 1 ) opt_render_links = 0; break; case ' ': if ( shift ) opt_single_time_step = true; else opt_single_frame = true; opt_pause = true; break; case 9: variable_control.switch_var_right(); break; case 96: variable_control.switch_var_left(); break; // `, until S-TAB works. case '-':case '_': variable_control.adjust_lower(); break; case '+':case '=': variable_control.adjust_higher(); break; default: printf("Unknown key, %d\n",ogl_helper.keyboard_key); break; } gravity_accel.y = opt_gravity ? -opt_gravity_accel : 0; lock_update(); // Update eye_direction based on keyboard command. // if ( user_rot_axis.x || user_rot_axis.y ) { pMatrix_Rotation rotall(eye_direction,pVect(0,0,-1)); user_rot_axis *= invert(rotall); eye_direction *= pMatrix_Rotation(user_rot_axis, M_PI * 0.03); modelview_update(); } // Update eye_location based on keyboard command. // if ( adjustment.x || adjustment.y || adjustment.z ) { const double angle = fabs(eye_direction.y) > 0.99 ? 0 : atan2(eye_direction.x,-eye_direction.z); pMatrix_Rotation rotall(pVect(0,1,0),-angle); adjustment *= rotall; switch ( opt_move_item ){ case MI_Ball: adj_vector = adjustment; if ( adj_t_stop == 0 ) adj_t_prev = adj_t_stop = world_time; adj_t_stop += adj_duration; break; case MI_Ball_V: balls_push(adjustment,0); break; case MI_Light: light_location += adjustment; break; case MI_Eye: eye_location += adjustment; break; default: break; } modelview_update(); } } void World::init() { chain_length = 14; opt_time_step_duration = 0.0003; variable_control.insert(opt_time_step_duration,"Time Step Duration"); distance_relaxed = 15.0 / chain_length; opt_spring_constant = 150; variable_control.insert(opt_spring_constant,"Spring Constant"); opt_gravity_accel = 9.8; opt_gravity = true; gravity_accel = pVect(0,-opt_gravity_accel,0); variable_control.insert(opt_gravity_accel,"Gravity"); opt_air_resistance = 0.04; variable_control.insert(opt_air_resistance,"Air Resistance"); world_time = 0; time_step_count = 0; last_frame_wall_time = time_wall_fp(); frame_timer.work_unit_set("Steps / s"); opt_shadows = true; opt_shader = SO_Fixed; ball_eye = NULL; opt_ride = false; init_graphics(); // Declared like a programmable shader, but used for fixed-functionality. // sp_fixed = new pShader(); sp_phong = new pShader ("hw03-shdr.cc",// File holding shader program. "vs_main(); ", // Name of vertex shader main routine. "gs_main_simple();", "fs_main();" // Name of fragment shader main routine. ); ball_setup_2(); lock_update(); } Ball* World::make_marker(pCoor position, pColor color) { Ball* const ball = new Ball; ball->position = position; ball->locked = true; ball->velocity = pVect(0,0,0); ball->radius = 0.2; ball->mass = 0; ball->contact = false; ball->color = color; return ball; } void World::lock_update() { // This routine called when options like opt_head_lock might have // changed. // Update locked status. // if ( head_ball ) head_ball->locked = opt_head_lock; if ( tail_ball ) tail_ball->locked = opt_tail_lock; // Re-compute minimum mass needed for stability. // for ( BIter ball(balls); ball; ) ball->spring_constant_sum = 0; const double dtis = pow( opt_time_step_duration, 2 ); for ( LIter link(links); link; ) { Ball* const b1 = link->ball1; Ball* const b2 = link->ball2; b1->spring_constant_sum += opt_spring_constant; b2->spring_constant_sum += opt_spring_constant; } for ( BIter ball(balls); ball; ) { ball->mass_min = ball->spring_constant_sum * dtis; ball->constants_update(); } } void World::balls_twirl() { if ( !head_ball || !tail_ball ) return; pNorm axis(head_ball->position, tail_ball->position); for ( BIter ball(balls); ball; ) { pVect b_to_top(ball->position,head_ball->position); const float dist_along_axis = dot(b_to_top,axis); const float lsq = b_to_top.mag_sq() - dist_along_axis * dist_along_axis; if ( lsq <= 1e-5 ) { ball->velocity = pVect(0,0,0); continue; } const float dist_to_axis = sqrt(lsq); pNorm rot_dir = cross(b_to_top,axis); ball->velocity += 2 * dist_to_axis * rot_dir; } } void World::objects_erase() { ball_eye = NULL; link_change = true; balls.erase(); links.erase(); } Links World::link_new(Ball *ball1, Ball *ball2) { Links links_rv; assert( ball1->radius > 0 ); assert( ball2->radius > 0 ); Link* const rlink = new Link(ball1,ball2); links_rv += rlink; pNorm n12(ball1->position,ball2->position); const float rad_sum = ball1->radius + ball2->radius; pMatrix3x3 b1rot = ball1->omatrix; pMatrix3x3 b2rot = ball2->omatrix; pCoor ctr = ball1->position + ( ball1->radius + 0.5 * ( n12.magnitude - rad_sum ) ) * n12; pNorm b1_y = b1rot * pVect(0,1,0); pNorm b1_x = b1rot * pVect(1,0,0); bool b1_dir_is_y = fabs(dot(b1_y,n12)) < 0.999; pNorm b1_dir = b1_dir_is_y ? b1_y : b1_x; pNorm con_x = cross(b1_dir,n12); pVect con_y = cross(n12,con_x); rlink->b1_dir = mult_MTV( b1rot, con_y ); rlink->b2_dir = mult_MTV( b2rot, con_y ); const float lrad = 0.2 * ball1->radius; for ( int i=0; i<3; i++ ) { const double theta = i * 2 * M_PI / 3; pVect convec = lrad * ( cos(theta) * con_x + sin(theta) * con_y ); pCoor con = ctr + convec; pVect cb1 = mult_MTV( b1rot, con - ball1->position ); pVect cb2 = mult_MTV( b2rot, con - ball2->position ); links_rv += new Link(rlink, cb1, cb2, 0); } return links_rv; } /// /// Physical Simulation Code /// /// Initialize Simulation // void World::ball_setup_1() { // Arrange and size balls to form a rectangular spiral. last_setup = 1; pCoor first_pos(13.4,10.8f,-9.2); // Remove objects from the simulated objects lists, balls and links. // The delete operator is used on objects in the lists. // objects_erase(); pNorm to_eye(first_pos,eye_location); pNorm to_rt = pVect(1,0,0); pNorm to_up = pVect(0,0,1); for ( int i=0; i<chain_length; i++ ) { // Construct a new ball and add it to the simulated objects list (balls). // Ball* const ball = balls += new Ball; pCoor ref_pos = i == 0 ? first_pos : balls[balls-2]->position; pVect dirs[4] = {to_rt,to_up,-to_rt,-to_up}; pVect dir = dirs[i&3]; // Initialize position and other information. // ball->position = ref_pos + (1+i/2) * distance_relaxed * dir; ball->locked = false; ball->velocity = pVect(0,0,0); ball->radius = 0.3; ball->contact = false; // If it's not the first ball link it to the previous ball. if ( i > 0 ) links += link_new( ball, balls[i-1] ); } // The balls pointed to by head_ball and tail_ball can be manipulated // using the user interface (by pressing 'h' or 't', for example). // Set these variables. // head_ball = balls[0]; tail_ball = balls[balls-1]; opt_head_lock = true; // Head ball will be frozen in space. opt_tail_lock = false; // Tail ball can move freely. setup_at_end(); } void World::ball_setup_2() { // Arrange balls to form sort of an umbrella. last_setup = 2; pCoor first_pos(17.2,14.8f,-20.2); pVect dir_dn(0.5,first_pos.y/8,0.5); pVect dir_x(3*distance_relaxed,0,0); pVect dir_z(0,0,3*distance_relaxed); // Remove objects from the simulated objects lists, balls and links. // The delete operator is used on objects in the lists. // objects_erase(); auto nb = [&] (pCoor pos) { Ball* const ball = new Ball; ball->position = pos; ball->locked = false; ball->velocity = pVect(0,0,0); ball->radius = 0.3; ball->contact = false; balls += ball; return ball; }; head_ball = nb(first_pos); for ( int j: {-1,1} ) for ( int i: {-1,0,1} ) { Ball* const ball = nb(first_pos - dir_dn + i * dir_x + j * dir_z ); if ( i != 0 ) links += link_new(head_ball,ball); if ( i != -1 ) links += link_new(balls[balls-2],ball); if ( j == 1 && i != 0 ) links += link_new(balls[balls-4],ball); } Ball* const tail_start = nb(first_pos - dir_dn); links += link_new(balls[balls-6],tail_start); links += link_new(balls[balls-3],tail_start); pCoor last_pos = tail_start->position; for ( int i=1; i<5; i++ ) { Ball* const ball = nb(last_pos - dir_dn * (0.5 + drand48()) ); links += link_new(balls[balls-2],ball); last_pos = ball->position; } tail_ball = balls[balls-1]; opt_head_lock = true; // Head ball will be frozen in space. opt_tail_lock = false; // Tail ball can move freely. setup_at_end(); } void World::ball_setup_3() { last_setup = 3; objects_erase(); setup_at_end(); } void World::ball_setup_4() { last_setup = 4; objects_erase(); setup_at_end(); } void World::ball_setup_5() { last_setup = 5; objects_erase(); setup_at_end(); } void World::setup_at_end() { } /// Advance Simulation State by delta_t Seconds // void World::time_step_cpu(double delta_t) { time_step_count++; // Smoothly move ball in response to user input. // if ( adj_t_stop ) { const double dt = min(world_time,adj_t_stop) - adj_t_prev; pVect adj = dt/adj_duration * adj_vector; balls_translate(adj,0); adj_t_prev = world_time; if ( world_time >= adj_t_stop ) adj_t_stop = 0; } for ( BIter ball(balls); ball; ) { assert( ball->fdt_to_do ); ball->force = ball->mass * gravity_accel; ball->torque = pVect(0,0,0); } for ( Link *link: links ) { if ( !link->is_simulatable ) continue; // Spring Force from Neighbor Balls // Ball* const ball1 = link->ball1; Ball* const ball2 = link->ball2; // Find position and velocity of the point where the link touches // the surface of ball 1 ... // pVect dir1 = ball1->omatrix * link->cb1; pCoor pos1 = ball1->position + dir1; pVect vel1 = ball1->velocity + ball1->point_rot_vel(dir1); // ... and ball 2. // pVect dir2 = ball2->omatrix * link->cb2; pCoor pos2 = ball2->position + dir2; pVect vel2 = ball2->velocity + ball2->point_rot_vel(dir2); // Construct a normalized (Unit) Vector from ball to neighbor // based on link connection points and ball centers. // pNorm link_dir(pos1,pos2); pNorm c_to_c(ball1->position,ball2->position); const float link_length = link_dir.magnitude; // Compute the speed of ball's end of link towards neighbor's end of link. // pVect delta_v = vel2 - vel1; float delta_s = dot( delta_v, link_dir ); // Compute by how much the spring is stretched (positive value) // or compressed (negative value). // const float spring_stretch = link_length - link->distance_relaxed; // Determine whether spring is gaining energy (whether its length // is getting further from its relaxed length). // const bool gaining_e = ( delta_s > 0.0 ) == ( spring_stretch > 0 ); // Use a smaller spring constant when spring is loosing energy, // a quick and dirty way of simulating energy loss due to spring // friction. // const float spring_constant = gaining_e ? opt_spring_constant : opt_spring_constant * 0.7; const float force_mag = spring_constant * spring_stretch; pVect spring_force_12 = force_mag * link_dir; // Apply forces affecting linear momentum. // ball1->force += spring_force_12; ball2->force -= spring_force_12; if ( ! link->is_surface_connection ) continue; // Apply torque. // ball1->apply_tan_force(dir1,link_dir,force_mag); ball2->apply_tan_force(dir2,link_dir,-force_mag); } /// /// Update Position of Each Ball /// for ( BIter ball(balls); ball; ) { if ( ball->locked ) { ball->velocity = pVect(0,0,0); ball->omega = pVect(0,0,0); continue; } // Update Velocity // // This code assumes that force on ball is constant over time // step. This is clearly wrong when balls are moving with // respect to each other because the springs are changing // length. This inaccuracy will make the simulation unstable // when spring constant is large for the time step. // const float mass = max( ball->mass, ball->mass_min ); pVect delta_v = ( ball->force / mass ) * delta_t; if ( platform_collision_possible(ball->position) && ball->position.y < 0 ) { const float spring_constant_plat = ball->velocity.y < 0 ? 100000 : 50000; const float fric_coefficient = 0.1; const float force_up = -ball->position.y * spring_constant_plat; const float delta_v_up = force_up / mass * delta_t; const float fric_force_mag = fric_coefficient * force_up; pNorm surface_v(ball->velocity.x,0,ball->velocity.z); const float delta_v_surf = fric_force_mag / mass * delta_t; if ( delta_v_surf > surface_v.magnitude ) { // Ignoring other forces? delta_v = pVect(-ball->velocity.x,delta_v.y,-ball->velocity.z); } else { delta_v -= delta_v_surf * surface_v; } delta_v.y += delta_v_up; } ball->velocity += delta_v; // Air Resistance // const double fs = pow(1+opt_air_resistance,-delta_t); ball->velocity *= fs; // Update Position // // Assume that velocity is constant. // ball->position += ball->velocity * delta_t; ball->omega += delta_t * ball->fdt_to_do * ball->torque; pNorm axis(ball->omega); // Update Orientation // // If ball isn't spinning fast skip expensive rotation. // if ( axis.mag_sq < 0.000001 ) continue; // Update ball orientation. // ball->orientation_set ( pQuat(axis,delta_t * axis.magnitude) * ball->orientation ); } } bool World::platform_collision_possible(pCoor pos) { // Assuming no motion in x or z axes. // return pos.x >= platform_xmin && pos.x <= platform_xmax && pos.z >= platform_zmin && pos.z <= platform_zmax; } /// External Modifications to State // // These allow the user to play with state while simulation // running. // Move the ball. // void Ball::translate(pVect amt) {position += amt;} // Add velocity to the ball. // void Ball::push(pVect amt) {velocity += amt;} // Set the velocity to zero. // void Ball::stop() {velocity = pVect(0,0,0); } // Set the velocity and rotation (not yet supported) to zero. // void Ball::freeze() {velocity = pVect(0,0,0); } void World::balls_translate(pVect amt,int b){head_ball->translate(amt);} void World::balls_push(pVect amt,int b){head_ball->push(amt);} void World::balls_translate(pVect amt) { for ( BIter ball(balls); ball; ) ball->translate(amt); } void World::balls_push(pVect amt) { for ( BIter ball(balls); ball; ) ball->push(amt); } void World::balls_stop() { for ( BIter ball(balls); ball; ) ball->stop(); } void World::balls_freeze(){balls_stop();} void World::render_link_1(Link *link) { /// HOMEWORK 3: Put solution to Problem 1 here. Ball *const ball1 = link->ball1; Ball *const ball2 = link->ball2; // Direction of link relative to center off ball. // pVect dir1 = ball1->omatrix * link->cb1; // Place on surface of ball where link connects. // pCoor pos1 = ball1->position + dir1; // Direction and connection location for ball 2. // pVect dir2 = ball2->omatrix * link->cb2; pCoor pos2 = ball2->position + dir2; pVect p1p2(pos1,pos2); pNorm p1p2n(p1p2); // Number of segments used to construct link. Each segment is // approximately a cylinder. // const int segments = 15; // Number of sides of each cylinder. // const int sides = 20; const float delta_tee = 1.0 / segments; // Radius of link. // const float rad = ball1->radius * 0.3; /// SOLUTION -- Homework 3 // Compute scale factors for texture. const float tex_margin = 0.1; const float tex_aspect_ratio = 8.5 / 11; const float page_width_o = 2.5; // Width of texture in object-space coords. const float tex_t_scale = link->distance_relaxed / page_width_o; const float tex_angle_scale = rad * tex_aspect_ratio / page_width_o; pNorm dirn1(dir1); pNorm dirn2(dir2); // Vectors used to describe the cubic Hermite curve. // pVect v1 = p1p2n.magnitude * dirn1; pVect v2 = p1p2n.magnitude * dirn2; // Convert link's local x and y axes to global coordinates. // pVect b1_ydir = ball1->omatrix * link->b1_dir; pVect b2_ydir = ball2->omatrix * link->b2_dir; pCoor pts[sides+1]; pVect vecs[sides+1]; glColorMaterial(GL_FRONT,GL_AMBIENT_AND_DIFFUSE); glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,color_red); glBegin(GL_TRIANGLE_STRIP); glColor3fv( color_light_gray ); for ( int i=0; i<=segments; i++ ) { const float t = i * delta_tee; const float t2 = t * t; const float t3 = t2 * t; // Cubic Hermite interpolation. // Compute point along core of link. // pCoor ctr = ( 2*t3 - 3*t2 + 1 ) * pos1 + (-2*t3 + 3*t2 + 0 ) * pos2 + (t3 - 2*t2 + t ) * v1 - (t3 - t2 ) * v2; // Compute direction of link at this point. // pNorm tan = ( 6*t2 - 6*t ) * pos1 + (-6*t2 + 6*t ) * pos2 + (3*t2 - 4*t + 1 ) * v1 - (3*t2 - 2*t ) * v2; // Compute local x and y axes for drawing a cylinder. // pVect ydir = (1-t) * b1_ydir + t * b2_ydir; pNorm norm = cross(tan,ydir); pVect binorm = cross(tan,norm); for ( int j=0; j<=sides; j++ ) { const float theta = j * ( 2 * M_PI / sides ); pCoor pt = pts[j]; pVect vec = vecs[j]; vecs[j] = cosf(theta) * norm + sinf(theta) * binorm; pts[j] = ctr + rad * vecs[j]; if ( i == 0 ) continue; /// SOLUTION -- Homework 3 glTexCoord2d (tex_margin + t * tex_t_scale, 0.5 + theta * tex_angle_scale ); glNormal3fv(vecs[j]); glVertex3fv(pts[j]); /// SOLUTION -- Homework 3 glTexCoord2d (tex_margin + (t-delta_tee)*tex_t_scale, 0.5 + theta * tex_angle_scale ); glNormal3fv(vec); glVertex3fv(pt); } } glEnd(); } void World::render_link_2(Link *link) { /// HOMEWORK 4: Put solution to Problem 1 in this routine // and else where. // Ball *const ball1 = link->ball1; Ball *const ball2 = link->ball2; // Direction of link relative to center off ball. // pVect dir1 = ball1->omatrix * link->cb1; // Place on surface of ball where link connects. // pCoor pos1 = ball1->position + dir1; // Direction and connection location for ball 2. // pVect dir2 = ball2->omatrix * link->cb2; pCoor pos2 = ball2->position + dir2; pVect p1p2(pos1,pos2); pNorm p1p2n(p1p2); // Number of segments used to construct link. Each segment is // approximately a cylinder. // const int segments = 15; // Number of sides of each cylinder. // const int sides = 20; const float delta_tee = 1.0 / segments; // Radius of link. // const float rad = ball1->radius * 0.3; // Compute scale factors for texture. const float tex_aspect_ratio = 8.5 / 11; const float page_width_o = 2.5; // Width of texture in object-space coords. const float tex_t_scale = link->distance_relaxed / page_width_o; const float tex_angle_scale = rad * tex_aspect_ratio / page_width_o; pNorm dirn1(dir1); pNorm dirn2(dir2); // Vectors used to describe the cubic Hermite curve. // pVect v1 = p1p2n.magnitude * dirn1; pVect v2 = p1p2n.magnitude * dirn2; // Convert link's local x and y axes to global coordinates. // pVect b1_ydir = ball1->omatrix * link->b1_dir; pVect b1_xdir = cross(b1_ydir,p1p2n); pVect b2_ydir = ball2->omatrix * link->b2_dir; pCoor pts[sides+1]; pVect vecs[sides+1]; /// SOLUTION -- Homework 4 pNorm c1c2(ball1->position,ball2->position); const float thr = 0.999; const bool straight_link = dot( c1c2, dirn1 ) > thr && dot( c1c2, dirn2 ) < -thr; /// SOLUTION -- Homework 4 Remove OpenGL glBegin command. pCoors coords; pVects norms; pVector<float> tcoords; if ( !straight_link || bo_s_num_vertices == 0 ) // SOLUTION for ( int i=0; i<=segments; i++ ) { const float t = i * delta_tee; const float t2 = t * t; const float t3 = t2 * t; // Cubic Hermite interpolation. // Compute point along core of link. // pCoor ctr = ( 2*t3 - 3*t2 + 1 ) * pos1 + (-2*t3 + 3*t2 + 0 ) * pos2 + (t3 - 2*t2 + t ) * v1 - (t3 - t2 ) * v2; // Compute direction of link at this point. // pNorm tan = ( 6*t2 - 6*t ) * pos1 + (-6*t2 + 6*t ) * pos2 + (3*t2 - 4*t + 1 ) * v1 - (3*t2 - 2*t ) * v2; // Compute local x and y axes for drawing a cylinder. // pVect ydir = (1-t) * b1_ydir + t * b2_ydir; pNorm norm = cross(tan,ydir); pVect binorm = cross(tan,norm); for ( int j=0; j<=sides; j++ ) { const float theta = j * ( 2 * M_PI / sides ); pCoor pt = pts[j]; pVect vec = vecs[j]; vecs[j] = cosf(theta) * norm + sinf(theta) * binorm; pts[j] = ctr + rad * vecs[j]; if ( i == 0 ) continue; /// SOLUTION -- Homework 4 // // Remove calls to glNormal3fv and glVertex3fv and replace with // the code that saves normals and coordinates in lists. Also // add code saving texture coordinates. tcoords += t * tex_t_scale; tcoords += 0.5 + theta * tex_angle_scale; norms += vecs[j]; coords += pts[j]; tcoords += ( t - delta_tee ) * tex_t_scale; tcoords += 0.5 + theta * tex_angle_scale; norms += vec; coords += pt; } } /// SOLUTION -- Homework 4 const bool bo_tco_empty = !link_bo_vtx; if ( !link_bo_vtx ) glGenBuffers(5,&link_bo_vtx); GLuint bo_vtx = straight_link ? link_bo_vtx_s : link_bo_vtx; GLuint bo_nrm = straight_link ? link_bo_nrm_s : link_bo_nrm; if ( !straight_link || !bo_s_num_vertices ) { if ( straight_link ) { bo_s_num_vertices = coords.size(); pMatrix_Translate center(-pos1); pMatrix_Rows rot_to_local ((1/rad)*b1_xdir, (1/rad)*b1_ydir, p1p2n/p1p2n.magnitude); link_s_to_local = rot_to_local * center; } glBindBuffer(GL_ARRAY_BUFFER, bo_vtx); glBufferData (GL_ARRAY_BUFFER, // Kind of buffer object. sizeof(coords[0])*coords.size(), coords.data(), GL_STATIC_DRAW); glBindBuffer(GL_ARRAY_BUFFER, bo_nrm); glBufferData (GL_ARRAY_BUFFER, // Kind of buffer object. sizeof(norms[0])*norms.size(), norms.data(), GL_STATIC_DRAW); } if ( bo_tco_empty ) { glBindBuffer(GL_ARRAY_BUFFER, link_bo_tco); glBufferData (GL_ARRAY_BUFFER, // Kind of buffer object. sizeof(tcoords[0])*tcoords.size(), tcoords.data(), GL_STATIC_DRAW); } const int num_vtx = straight_link ? bo_s_num_vertices : coords.size(); if ( straight_link ) { // Multiply modelview matrix by a matrix that will transform the // coordinates of the straight links that we saved in the buffer // objects link_bo_vtx_s and link_bo_nrm_s to approximately // match the coordinates of the straight link we need to render // now. glMatrixMode(GL_MODELVIEW); glPushMatrix(); pMatrix_Translate center(pos1); pMatrix_Cols rot_to_global(rad*b1_xdir, rad*b1_ydir, p1p2); pMatrix m = center * rot_to_global* link_s_to_local; glMultTransposeMatrixf(m); } glColor3fv( straight_link ? color_pale_green : color_light_gray ); glEnableClientState(GL_VERTEX_ARRAY); glBindBuffer(GL_ARRAY_BUFFER, bo_vtx); glVertexPointer( 3, GL_FLOAT, sizeof(coords[0]), NULL); glEnableClientState(GL_NORMAL_ARRAY); glBindBuffer(GL_ARRAY_BUFFER, bo_nrm); glNormalPointer( GL_FLOAT, 0, NULL ); glEnableClientState(GL_TEXTURE_COORD_ARRAY); glBindBuffer(GL_ARRAY_BUFFER, link_bo_tco); glTexCoordPointer(2,GL_FLOAT,0,NULL); glDrawArrays(GL_TRIANGLE_STRIP, 0, num_vtx ); glDisableClientState(GL_NORMAL_ARRAY); glDisableClientState(GL_VERTEX_ARRAY); glDisableClientState(GL_TEXTURE_COORD_ARRAY); glBindBuffer(GL_ARRAY_BUFFER, 0); if ( straight_link ) { glPopMatrix(); } /// SOLUTION -- Homework 4, above } void World::frame_callback() { // This routine called whenever window needs to be updated. frame_timer.phys_start(); const double time_now = time_wall_fp(); if ( !opt_pause || opt_single_frame || opt_single_time_step ) { /// Advance simulation state. // Amount of time since the user saw the last frame. // const double wall_delta_t = time_now - last_frame_wall_time; // Compute amount by which to advance simulation state for this frame. // const double duration = opt_single_time_step ? opt_time_step_duration : opt_single_frame ? 1/30.0 : wall_delta_t; const double world_time_target = world_time + duration; const double wall_time_limit = time_now + 0.05; while ( world_time < world_time_target ) { time_step_cpu(opt_time_step_duration); world_time += opt_time_step_duration; const double time_right_now = time_wall_fp(); if ( time_right_now > wall_time_limit ) break; } // Reset these, just in case they were set. // opt_single_frame = opt_single_time_step = false; } last_frame_wall_time = time_now; if ( opt_ride && ball_eye ) { pNorm b_eye_down(ball_eye->position,ball_down->position); pVect b_eye_up = -b_eye_down; pCoor eye_pos = ball_eye->position + 2.2 * ball_eye->radius * b_eye_up; pNorm b_eye_direction(eye_pos,ball_gaze->position); pNorm b_eye_left = cross(b_eye_direction,b_eye_up); pMatrix_Translate center_eye(-eye_pos); pMatrix rotate; rotate.set_identity(); for ( int i=0; i<3; i++ ) rotate.rc(0,i) = b_eye_left.elt(i); for ( int i=0; i<3; i++ ) rotate.rc(1,i) = b_eye_up.elt(i); for ( int i=0; i<3; i++ ) rotate.rc(2,i) = -b_eye_direction.elt(i); modelview = rotate * center_eye; pMatrix reflect; reflect.set_identity(); reflect.rc(1,1) = -1; transform_mirror = modelview * reflect * invert(modelview); } render(); } int main(int argv, char **argc) { pOpenGL_Helper popengl_helper(argv,argc); World world(popengl_helper); glDisable(GL_DEBUG_OUTPUT); glDebugMessageControl(GL_DONT_CARE,GL_DONT_CARE, GL_DEBUG_SEVERITY_NOTIFICATION,0,NULL,false); popengl_helper.rate_set(30); popengl_helper.display_cb_set(world.frame_callback_w,&world); }